Starbucks’ campaign to get customers chatting about race is sparking plenty of conversations — just maybe not the type envisioned by Chief Executive Howard Schultz.

After Starbucks unveiled the “Race Together” campaign to get employees and customers talking about the often sensitive and personal topic, people have taken to Facebook and Twitter to pass judgement. Social-media conversations about Starbucks among the general public increased nearly threefold on Tuesday, a day after the campaign was introduced, compared with the average volume in the last month, according to data from social media analytics firm Networked Insights. There were about 79,000 mentions of Starbucks across the social web on Tuesday, Networked Insights said.

The trouble for Starbucks is that about 58% of those social-media mentions have been negative, and more than a third of consumers’ online conversations were categorized as “hate,” Networked Insights found. Among conversations falling in the “hate” category, many consumers called out issues behind the execution of the campaign and anger towards Mr. Schultz, the research firm said.

Earlier this week, Mr. Schultz asked Starbucks employees to write “Race Together” on coffee cups as “an opportunity to begin to re-examine how we can create a more empathetic and inclusive society – one conversation at a time,” according to a company statement.

Some consumers were supportive of the campaign’s intentions — 7% of online responses can be can be characterized as “empathy,” Networked Insights said.

Meanwhile, Networked Insights’ analysis of marketers on social media found that 62% of their posts about Starbucks in the days following the campaign’s announcement were negative and highly critical of the company.